An Analysis of the 'Failed States Index' by Partial Order Methodology

By Carlsen, Lars; Brüggemann, Rainer | Journal of Social Structure, January 1, 2013 | Go to article overview

An Analysis of the 'Failed States Index' by Partial Order Methodology


Carlsen, Lars, Brüggemann, Rainer, Journal of Social Structure


(ProQuest: ... denotes formula omitted.)

Introduction

Often objects are to be ranked without an available measurable quantity, expressing the ranking aim. Typically a set of indicators is then selected, where the indicators are considered as proxies for the ranking aim (this set of indicators is often called an information basis, IB). Definition and quantifying these indicators are difficult and time expensive. Therefore the multi-system of indicators (MIS: multi-indicator system) is of high value for its own right. Nevertheless a ranking on the basis of a MIS cannot directly be performed. Therefore in many ranking methods an aggregation of these indicators is performed, for example by determining the weighted sum of indicator values of each object.

Obviously, provided a one-dimensional scale after any aggregation such as a simple addition of the single indicators, ranking is easy and straightforward. However, what are the consequences of this simplicity? In the best case some valuable information is lost. More unfortunate is that such a simple addition of the indicator values may lead to quite erroneous conclusions as high score(s) in certain indicator(s) may be leveled off by low scores in other indicator(s), without taking into account that these indicators point towards quite different topics albeit expressing the same ranking aim. In plain words such a simple addition is adding apples and oranges, the eventual result being bananas ranked according to their length. This is a general problem, which holds to a different extent for all multicriteria decision tools and is called the degree of compensation (Munda, 2008). Compensation effects appear to different degrees in all decision support systems where a set of indicators is mapped onto a single scale. Munda (2008) analyzes many of the often used multicriteria decision methods and he founds that the construction of composite indicators by weighted sums of individual ones has the highest degree of compensation.

In this paper a methodology is presented, which is based on simple elements of partial order theory. Partial order theory is considered as a discipline of Discrete Mathematics. The central idea is, to avoid any mapping of indicators on a single scale and extract as much information from the set of indicators respecting at the same time the ranking aim. Partial order theory also provides a technique to derive rankings (where ties are not excluded), which avoids the need of a weighting of the indicators of the information basis. We will outline basics of this theory in the methodology.

As an example we selected the Failed State Index from 2011 (FFP, 2013a), which is generated as a sum of twelve individual indicators, serving as proxy for the not immediately accessible ranking aim ?Failed Nations? (or in a dual sense: ?Stabilization of nations?) (see below).

Methodology

Multi-Indicator Systems

In a multi-indicator system (MIS) the main part of information about the objects is the setting of the indicators and their quantification to obtain appropriate indicator values for the single objects under investigation. In many multicriteria decision systems this valuable and detailed information is mapped onto a single constructed indicator, whereby the information, originally included in the MIS is lost. However, in general metric information is kept.

Partial order theory applied on a MIS is an alternative way to analyze the MIS by keeping the information of the set of indicators, but by providing ordinal information instead of a metric one.

Partial Order

The analysis of partially ordered sets (posets) is a relatively new branch in Discrete Mathematics. The first steps were taken at the end of the 19th century, but only in the mid of the 20th it received a more widespread attention in mathematics. The contributions of Birkhoff (1984) and of Hasse (1967) may be considered as important mile stones. In physics and mathematical chemistry partial order plays some role (see e. …

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